Reply to Lazaridis and Reich: Robust model-based inference of male-biased admixture during Bronze Age migration from the Pontic-Caspian Steppe.

By comparing the sex-specifically inheritedX chromosome to the autosomes in ancient genetic samples,we (1) studied sex-specific admixture for two prehistoric migrations. For each migration we used several admixture estimation procedures—including ADMIXTURE model-based clustering (2)—to compare X-chromosomal and autosomal ancestry in contemporaneous Central Europeans and we interpreted greater admixture from the migrating population on the autosomes asmale-biasedmigration. Formigration into late Neolithic/Bronze Age Central Europeans (BA) from the Pontic-Caspian Steppe (SP) we inferred malebiased admixture at 5–14 males per migrating female. Lazaridis and Reich (3) contest this male-biased migration claim. For simulated individuals, they claim that ADMIXTURE provides biased X-chromosomal ancestry estimates. They argue that if the bias is taken into account, then X-chromosomal steppe ancestry is similar to our autosomal ancestry estimate, and that hence steppe male and female contributions are similar. Many factors affect ancestry inferences from ADMIXTURE and related programs (2, 4–8). To understandADMIXTURE inferences for X-chromosomal ancient DNA, we performed simulations examining the effects of multiple variables. First, we used “reference” individuals in ref. 1 to simulate analogs of the BA population. Fig. 1 plots estimated X-chromosomal ancestry for simulated BA individuals (Fig. 1 A and B), showing that for high true ancestry levels ADMIXTURE overestimates steppe ancestry, whereas for low levels it underestimates it. For the intermediate ancestry in ref. 1 (0.366), however, ADMIXTURE is accurate, and our estimate is robust to bias. Because our interest in ref. 1 was the X/autosomal comparison, we next simulated autosomes, finding bias similar to that of the X chromosome (Fig. 1C andD). Bias-corrected X/autosomal ancestry estimates translate in a constant-admixture model (1) to four to seven migrating steppe males per female. Thus, accounting for ADMIXTURE bias, substantial male excess during the steppe migration remains supported. We next tested whether specific data features—haploid ancient genotypes, highmissing-data rates, and small reference samples—might underlie previously unseen ADMIXTURE biases. We performed analogous simulations using modern HapMap samples without these features. This analysis traces the bias to the small reference samples available in haploid ancient data (1) (Fig. 2). The greater bias in ADMIXTURE in ref. 3 than here thus likely arises from two sources. First, ancestry values underlying the simulation in ref. 3 trend toward parameter values that generate higher bias than with our even spacing. Second, ADMIXTURE inference in ref. 3 discards one individual per source population, potentially enlarging bias from small reference samples. We note that the authors of ref. 3 also consider a second program, qpAdm (9); their wide confidence intervals for this summary-statistic method relying on f4 calculations permit multiple interpretations (male bias, female bias, or no bias). Direct f4 calculation (10), however, trends toward male-biased migration: BA share more alleles with SP than with early Neolithic Central Europeans (CE) on autosomes [f4(chimp,BA;CE,SP) = 0.0014; Z = 6.78, P < 0.0001], but have more CE X-chromosomal sharing (f4 = −0.0068; Z = −0.561). We conclude that our inference ofmale-biasedPonticCaspian Steppe migration, seen using ADMIXTURE, STRUCTURE, mechanistic simulations, and X/autosomal FST, is robust. Our analysis further illuminates the impact of small haploid reference samples on ADMIXTURE; we look forward to refining sex-specific migration estimates as larger, higher-coverage ancient samples become available.